Good lattice rules are an important type of quasi-Monte Carlo algorithms. They are known to have good theoretical properties, in the sense that they can achieve an error bound (or optimal error bound) that is independent of the dimension for weighted spaces with suitably decaying weights. To use the theory of weighted function spaces for practical applications, one has to determine what weights...

We calculate the probability distributions for the number of occurrences n of of a given l letter word in a random string of k letters. We consider the case in which the letters of the strings belong to an r letter alphabet. Analytical expressions for the distribution are known for the asymptotic regimes (i) k ≫ r ≫ 1 (Gaussian) and k, l → ∞ such that k/r is finite (Compound Poisson). However, ...

We test the asymptotic scaling behaviour of state-of-the-art simulations of QCD with two flavors of light Wilson fermions. This is done by matching π and ρ masses on lattices of size 16 × 32 and 8 × 16. We find that at β = 6/g = 5.3 matching is not possible over a range extending down to β = 3.5. The large lattice data at β = 5.5 matches the small lattice values at β = 4.9(1) leading to a shift...

In this work a static quark-antiquark potential that is valid for all quark-antiquark separations is constructed. By matching the long range results from lattice QCD to a short range perturbative part we get a continuous potential expression. The lattice part is obtained by tting an analytic potential model to lattice data for di erent lattice spacings a. Extrapolating the tting parameters to t...

We reconsider the construction and matching of the vector and axial currents in Wilson Chiral Perturbation Theory (WChPT), the low-energy effective theory for lattice QCD with Wilson fermions. In particular, we discuss in detail the impact of the finite renormalization of the currents on their matching from the lattice theory to WChPT. We explicitly show that imposing chiral Ward-Takahashi iden...

The SPEAR 3 Upgrade Project seeks to replace the present 160 nm-rad FODO lattice with an 18 nm-rad double bend achromat (DBA) lattice. The new lattice must conform to the layout of the SPEAR racetrack tunnel and service the existing photon beamlines. Working within these constraints, we designed a lattice with 18 achromatic cells and 3 GeV beam energy. This paper reports on design of the main D...